The 18-year-old winger became the youngest player in the history of Brazil's national championship when he made his senior debut at the age of 15 years and 308 days.
Gabriel's fee and the length of his contract have not been confirmed, although reports have suggested he has cost the Premier League club around £13 million ($17m).
"Welcome to Chelsea, Angelo!" said a statement Sunday on the club's official website.
Angelo arrives at the London club after making 129 appearances for Santos across all competitions, scoring five goals and making 10 assists. He is also the youngest player to score in Copa Libertadores history.
Information from Reuters and The Associated Press was used in this story.